# Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

^{3}.

#### 2.2. Methodology

#### 2.2.1. The Cauchy Distribution

#### 2.2.2. Multi-Fractional Generalized Cauchy Model

#### 2.2.3. Statistical Analysis

## 3. Results

#### 3.1. Descriptive Statistics of Sea Surface Chlorophyll Concentration Series

^{3}and 0.0932–33.0401 mg/m

^{3}, respectively, among the two groups of data, which are the closest locations to the Pearl River estuary and Yangtze River estuary. The range of the sea surface chlorophyll concentration decreases with distance concerning to the two estuaries. Moreover, the mean values and standard deviation values had the similar decreasing trends from the estuaries to offshore locations. According to the LSD-t results, there are significant differences in the mean sea surface chlorophyll concentration values among M1, M2, M3, and M6 at a 0.05 significance level. Conversely, the mean values of M3, M4, and M5 (or M4, M5, and M6) do not exhibit significant differences at the 0.05 significance level. On another note, the mean sea surface chlorophyll concentration values at N1, N2, N3, N4, and N5 (or N6) display significant variations, while the mean values at N5 and N6 do not differ significantly from each other at the 0.05 significance level.

#### 3.2. Variability of the Long-Range Dependence of Sea Surface Chlorophyll Series

#### 3.3. Monthly and Seasonal Variations in Hurst Exponents for Sea Surface Chlorophyll

## 4. Discussion

#### 4.1. The Impact of Anthropogenic Activity on the Long-Range Dependence of Sea Surface Chlorophyll Concentration

#### 4.2. Seasonal Variation in the Long-Range Dependence of Sea Surface Chlorophyll Concentration

#### 4.3. Limitations and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The distribution of the 12 studied locations for sea surface chlorophyll concentrations. The dash line presents the administrative boundary of China.

**Figure 2.**Temporal variations in daily sea surface chlorophyll concentrations at the 12 studied locations during the period from December 2017 to November 2023.

**Figure 3.**Hurst exponent variations in daily sea surface chlorophyll concentrations at the 12 studied locations during the period from December 2017 to November 2023.

**Figure 4.**Monthly Hurst exponent values of daily sea surface chlorophyll concentrations at (

**a**) M1, M2, …, M6 locations and (

**b**) N1, N2, …, N6 locations during the period from December 2017 to November 2023. The yellow lines with circles represent the monthly averaged values of Hurst exponent values. The letters in each subfigure represent the differences by using the LSD test at a 0.05 significance level.

**Figure 5.**Seasonal Hurst exponent values of daily sea surface chlorophyll concentrations at the 12 studied locations during the period from December 2017 to November 2023. The yellow lines with circles represent the seasonal averaged values of Hurst exponent values. The letters in each subfigure represent the differences by using the LSD test at a 0.05 significance level.

**Table 1.**The descriptive statistical results for the series of daily sea surface chlorophyll concentrations and Hurst exponents at the 12 studied locations during the period from December 2017 to November 2023.

ID | Chl_Minimum | Chl_Maximum | Chl_Mean ± Standard Deviation | Chl_Coefficient of Variation | H_Mean ± Standard Deviation |
---|---|---|---|---|---|

M1 | 0.1356 | 50.8658 | 4.5975 ± 3.7523 a* | 0.8161 | 0.0797 ± 0.0899 a |

M2 | 0.0607 | 3.6647 | 0.2889 ± 0.2192 b | 0.7588 | 0.4072 ± 0.0999 b |

M3 | 0.0463 | 1.6592 | 0.1607 ± 0.0914 c | 0.5683 | 0.5016 ± 0.0831 c |

M4 | 0.0437 | 0.5228 | 0.1239 ± 0.0541 cd | 0.4362 | 0.5286 ± 0.0729 d |

M5 | 0.0467 | 1.1772 | 0.1181 ± 0.0589 cd | 0.4986 | 0.5391 ± 0.0703 e |

M6 | 0.0437 | 1.4624 | 0.1123 ± 0.0490 d | 0.4362 | 0.5431 ± 0.0690 f |

N1 | 0.0932 | 33.0401 | 3.5173 ± 2.2694 a | 0.6452 | 0.0948 ± 0.0889 a |

N2 | 0.0976 | 21.5406 | 0.8885 ± 0.9993 b | 1.1247 | 0.2749 ± 0.1179 b |

N3 | 0.0730 | 5.1777 | 0.3253 ± 0.2959 c | 0.9096 | 0.3957 ± 0.1010 c |

N4 | 0.0324 | 0.4974 | 0.1178 ± 0.0482 d | 0.4097 | 0.5276 ± 0.0615 d |

N5 | 0.0206 | 0.3076 | 0.0795 ± 0.0342 e | 0.4302 | 0.5601 ± 0.0682 e |

N6 | 0.0244 | 0.2237 | 0.0604 ± 0.0206 e | 0.3411 | 0.5909 ± 0.0674 f |

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**MDPI and ACS Style**

He, J.; Li, M.
Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea. *Fractal Fract.* **2024**, *8*, 102.
https://doi.org/10.3390/fractalfract8020102

**AMA Style**

He J, Li M.
Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea. *Fractal and Fractional*. 2024; 8(2):102.
https://doi.org/10.3390/fractalfract8020102

**Chicago/Turabian Style**

He, Junyu, and Ming Li.
2024. "Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea" *Fractal and Fractional* 8, no. 2: 102.
https://doi.org/10.3390/fractalfract8020102